First n natural number are 1,2,3,n.
`"Mean, "barx=((1+2+3+...+n))/(n)=(1)/(n)cdot(1)/(2)n(n+1)=(1)/(2)(n+1)" "[because (1+2+3+...+n)=(1)/(2)n(n+1)]`
`therefore" variance," sigma^(2)=(Sigmax_(i)^(2))/(n)-barx^(2)`
`=(Sigman^(2))/(n)-{(1)/(2)(n+1)}^(2)`
`=(1)/(n)cdot(n(n+1)(2n+1))/(6)-(1)/(4)(n+1)^(2)" "[because Sigman^(2)=(1)/(6)n(n+1)(2n+1)]`
`={((b+1)(2n+1))/(6)-((n+1)^(2))/(4)}`
`=(n+1)cdot{((2n+1))/(6)-((n+1))/(4)}`
`=((n+1)(n-1))/(12)=((n^(2)-1))/(12).`
`therefore" variance,"sigma^(2)=((n^(2)-1))/(12).`
Standard deviation, `sigma=sqrt((n^(2)-1)/(12))=(1)/(2).sqrt((n^(2)-1)/(3)).`
